Ab Initio Study of Silyloxonium Ions

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Ab Initio Study of Silyloxonium Ions Organometallics, Vol. 16, No. 26, 1997 5947 Table 5. Calculated Proton Affinities (6-31G*) of Model Oxygen Bases (Eq 13) (kcal/mol) a base ∆E0 e (HF) ∆E0 e (MP2) ∆E0 e (MP3) ∆E0 e (MP4) ∆E298 b ∆H298 c ∆S (cal/(mol K)) ∆G298 c 4a -189.6 -189.2 -191.8 -191.1 5.8 -185.3 -27.9 -177.0 5a -190.7 -187.8 -190.4 -189.3 5.6 -183.7 -14.1 -179.5 6a -192.8 -192.6 194.7 194.4 5.7 -188.7 -36.1 -178.0 7a -203.4 -200.5 -203.4 -201.9 5.9 -196.0 -23.2 -189.1 8a d -199.3 -195.2 -197.1 196.5 6.5 -189.9 -21.8 -183.4 9a d -197.9 -194.6 -197.1 196.1 6.1 -190.0 -21.8 -183.5 a S(H + ) ) 26.039 cal/(mol K). 35 b ∆E298 ) E298 vib + ∆E298 rot + ∆E298 trans + ∆(PV); ∆E298 vib scaled by 0.893. 8 c Based on the MP4/6-31G*/ /6-31G* energies. d HF, MP2, and MP3 values taken from ref 16b. Figure 3. Plot of the silylenium cation affinity vs the proton affinity of several siloxanes (kcal/mol). similar correlation is found between the silicophilicity and basicity scale. This is in accord with the linear relationship between proton and Me3Si + affinities found previously by ICR measurements. 31 The linear correlation between proton and silyl affinities suggests that the electronic demands of both cations are similar; that is, they induce analogous changes in the electronic structure of a siloxane base. The lower energy of interaction with silylenium cation is mainly due to the higher thermodynamic stability of H3Si + relative to H + . Thus, protonation causes greater changes in the molecular structure of a siloxane than does silylation. Cyclotrisiloxane 5a is 4 kcal/mol more silicophilic than 4a. This is consistent with the known high reactivity of its permethylated analogue. 3 The high basicity and silicophilicity of oxadisilacyclopentane 7a results from two main factors. (i) The geometry of the five-membered ring does not allow optimal orbital overlap. Consequently, the n(O)fσ*- (Si-X) delocalization is diminished (the total NBO delocalization energy associated with these interactions is 35.3 kcal/mol in 7a, compared to 47.9 and 42.4 kcal/ mol in 4a and 5a, respectively), and the oxygen lone pairs are thus more localized. The calculated energy of the HOMO is higher than in other siloxanes (-11.3 eV in 7a, compared to -12.1 eV in 4a and -11.8 eV in 5a). (ii) The enthalpy of protonation or silylation of 7a involves an energy gain due to the release of ring strain. Studies of the Protonation of Siloxanes in Solution. Since polymerization is usually carried out in solution, we have attempted to estimate computationally the effect of solvation on the thermodynamics of the Scheme 3 Table 6. Relative Basicities (6-31G*) of Model Oxygen Bases Calculated Using Disiloxane 4a as a Reference Base (kcal/mol) base ∆E0 e (HF) ∆E0 e (MP2) ∆E0 e (MP3) ∆E0 e (MP4) ∆H298 a ∆G298 a 4a 0 0 0 0 0 0 5a 1.1 -1.4 -1.4 -1.8 -1.6 2.5 6a 3.2 3.5 3.3 3.4 2.4 1.1 7a 13.8 11.3 11.6 10.8 10.7 12.1 8a b 9.7 6.0 5.3 5.4 4.6 6.4 9a b 8.3 5.4 5.3 5.0 4.7 6.5 a Based on the MP4/6-31G*//6-31G* energies. b HF, MP2, and MP3 values taken from ref 16b. protonation reaction employing a SCRF method. 15 As model solvents for calculations we chose cyclohexane (ɛ ) 2.0) and dichloromethane (ɛ ) 8.9), which have been commonly used in mechanistic studies of polymerization processes and which are believed to simulate closely the true conditions of polymerization. 3 The thermodynamic cycle shown in Scheme 3 was considered: 33 ∆H prot,s )-PA + ∆H s (BH + ) - ∆H s (B) - ∆H s (H + ) (15) The energy of solvation of ions may be expressed as a sum of two components: (i) the neutral term (involving cavitation and dispersion-repulsion interactions) and (ii) the electrostatic term (eq 16). 33 ∆Hs (BH + ) ) neutral term + electrostatic term ≈ el + ∆Hs (B) + ∆Hs (BH ) (16) The first term was found to be nearly the same for neutral and protonated amines in water (the difference being less than 0.2 kcal/mol); therefore, it seems reasonable to assume that this is also true for siloxanes in cyclohexane and dichloromethane. 33b Thus el + el ∆Hprot,s )-PA + ∆Hs (BH ) - ∆Hs (B) - ∆Hs (H + ) (17) The equilibrium geometries calculated for 4a and 5a in cyclohexane and dichloromethane using the Onsager dipole model are almost identical with the gas-phase geometries (differences in bond lengths and angles are less than 0.001 Å and less than 0.1°, respectively, except (33) (a) Aue, D. H.; Webb, H. M.; Bowers, M. T. J. Am. Chem. Soc. 1976, 98, 318. (b) Tuñon, I.; Silla, E.; Tomasi, J. J. Phys. Chem. 1992, 96, 9043.
5948 Organometallics, Vol. 16, No. 26, 1997 Cypryk and Apeloig Table 7. Calculated Thermodynamic Properties (6-31G*) for the Addition of H3Si + to Model Oxygen Bases (Eq 15) (kcal/mol) a base ∆E0 e (HF) ∆E0 e (MP2) ∆E0 e (MP3) ∆E0 e (MP4) ∆E298 b ∆H298 c ∆S (cal/(mol K)) ∆G298 c 4a -59.7 -69.5 -69.0 -70.0 2.5 -67.5 -45.3 -54.0 5a -60.0 -68.6 -67.9 -68.8 2.4 -66.4 -28.3 -58.0 6a d -61.7 -72.7 2.5 -70.2 -49.8 -55.3 7a -73.8 -81.0 -80.7 -81.0 2.5 -78.5 -32.5 -68.8 8a -70.0 -75.8 -74.3 -75.4 2.7 -72.7 -28.9 -64.1 9a -67.7 -74.8 -74.0 -74.7 2.6 -72.1 -28.5 -63.6 a SiH3 + : E0 e (HF) )-290.328 91; E0 e (MP2) )-290.391 21; E0 e (MP3) )-290.406 03. E0 e (MP4) )-290.410 57; ∆E298 ) 15.4 kcal/mol; S ) 48.88 cal/(mol K). b ∆E298 ) E298 vib + ∆E298 rot + ∆E298 trans + ∆(PV); ∆E298 vib scaled by 0.893. 8 c Based on the MP4/6-31G*//6-31G* energies, unless stated otherwise. d ∆H and ∆G were calculated using MP2/6-31G* values. Table 8. Relative Silicophilicities (6-31G*) of Model Oxygen Bases 4a-9a, using Disiloxane 4a as a Reference (kcal/mol) base ∆E0 e (HF) ∆E0 e (MP2) ∆E0 e (MP3) ∆E0 e (MP4) ∆H298 a ∆G298 a 4a 0 0 0 0 0 0 5a 0.3 -0.9 -1.1 -1.2 -1.1 4.0 6a b 2.0 3.2 2.7 1.3 7a 14.1 11.5 11.7 11.0 11.0 14.8 8a 10.3 6.3 5.3 5.4 5.2 10.1 9a 8.0 5.3 5.0 4.7 4.6 9.6 a Based on the MP4/6-31G*//6-31G* energies, unless stated otherwise. b ∆H and ∆G were calculated using the MP2/6-31G* values. for the Si-O-Si angle, which decreases from 170.0° in the gas phase to 168.9° in C6H12 and 167.6° in CH2Cl). This is not surprising, as the dipole moments of siloxanes are close to zero. Changes in the equilibrium geometries of protonated siloxanes 4b and 5b upon solvation are somewhat larger (differences in bond lengths and bond angles are less than 0.005 Å and 0.2°, respectively). However, these changes do not significantly affect the energies of the protonated species. For example, the energies calculated for 5b in CH2Cl2 using gas-phase and SCRF geometries differ by only 0.3 kcal/ mol. In view of the above, the gas-phase geometries were used for calculations of the solvent effects. Moreover, the thermal corrections to enthalpy and free energy calculated for 4a and 4b in solution are very similar to those calculated in the gas phase ((∆E298)s < 0.1 kcal/mol, T∆Ss < 0.2 kcal/mol). Assuming that this holds also for 5a-7a, the following approximation can be made: el + el + el + ∆Hs (BH ) ) Hs (BH ) - Hg (BH ) ≈ el + el + Es (BH ) - Eg (BH ) (18) Hence, the relative proton affinity in solution of the bases B1 and B is given by eq 19. The relative basicities el + ∆Hprot,s (B) - ∆Hprot,s (B1 ) )-∆PA + ∆Es (BH ) - el ∆Es (B1H + el el ) - (∆Es (B) - ∆Es (B1 )) (19) (∆Gprot,s(B) - ∆Gprot,s(B1)) of siloxanes in solution were calculated from an equation analogous to eq 19. The results of such calculations for 4a-7a are presented in Table 9. The basicity order of siloxanes in both cyclohexane and in dichloromethane is 7a > 4a > 5a > 6a. The differences between the two solvents are small (Table 9). In the gas phase, the order is 7a > 5a > 6a > 4a. As in the gas phase, also in solution 7a is much more basic than the other siloxanes, which indicates the dominance of structural effects (mostly angular strain) in this case. The basicity order of the other siloxanes in solution is different from that in the gas phase, 4a being more basic in solution than 5a and 6a. Since no experimental data are available for hydrogensubstituted siloxanes, the closest comparison which can be made is with dimethylsiloxanes. In the gas phase, the basicity of methyl siloxanes relative to their H analogues is mainly determined by their higher polarizability, which increases with increasing size of the molecule. 16a,b,30 In solution, the basicity order of dimethylsiloxanes was measured by two types of reactions: first, as constants for hydrogen bonding with phenol in CCl4 29a and with CF3COOH in CH2Cl2. 29b In these experiments the basicity order D3 > D4 > (Me3- Si)2O was found. On the other hand, the interaction of dimethylsiloxanes with CF3SO3H in the presence of a reference base (hindered amine) in C6H6 gave the basicity order (Me3Si)2O > D3 ≈ D4. 29c The different basicity order is not unexpected, as the reactions used for these measurements are significantly different. In hydrogen bonding (e.g. with phenol) only partial proton transfer occurs, whereas interaction with CF3SO3H, which is one of the strongest protonic acids, involves a much larger degree of proton transfer, resulting probably in ion-pair formation. The reaction with CF3SO3H probably models more closely the “full” protonation considered here, and indeed, the basicity order measured using CF3SO3H corresponds well to the basicity order calculated by us. These studies clearly show that the basicities of siloxanes depend on the reaction system, particularly on the polarity and donor-acceptor properties of the solvent and on the strength of a reference acid used for such measurements. 29 Implications of the Calculations for the Polymerization Mechanism of Cyclic Siloxanes. The differences in basicities are expected to cause changes in the kinetics and mechanism of polymerization. For example, the basicity of a cyclic monomer relative to that of a siloxane oxygen within a polymer chain determines the proportion of propagation vs undesired chain scission. Oxadisilacyclopentane 7a, the most basic and more silicophilic among the cyclosiloxanes discussed here, is expected to be the most reactive monomer. Its high strain energy indicates that polymer formation is strongly thermodynamically favored. Cyclotrisiloxane 5a is expected to be less reactive, but its moderate ring strain also highly favors polymerization. In contrast, cyclotetrasiloxane 6a has basicity and silicophilicity similar to that of the siloxane chain (which is modeled by 4a) and the enthalpy of its ring-opening reaction is close to zero. Hence, the polymerization of 6a is expected to lead to equilibration, i.e., to a thermodynamic mixture of cyclic and linear siloxanes, as is
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Ab Initio Study of Silyloxonium Ions

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